the combined effects of soil, water and surcharge … · 2019. 10. 27. · jekayinfa, s.o. and...

Jekayinfa, S.O. and Olawuni, O.E./LAUTECH Journal of Engineering And Technology 7(2)2013: 37 – 52

THE COMBINED EFFECTS OF SOIL, WATER AND SURCHARGE LOADS ON THE STRUCTURAL BEHAVIOURS OF CANTILEVER

RETAINING WALL

Adedokun, S. I. and Oluremi, J. R.

Department of Civil Engineering, Ladoke Akintola University of Technology, P.M.B. 4000, Ogbomoso. Oyo State. Correspondence Author: [email protected]; Tel: +234-806-232-8259

ABSTRACT Retaining walls are engineering structures constructed to resist lateral forces imposed by soil movement and water pressure; they are used as protection against the erosive forces of water and as a method of slope stabilization along highways, railroads and construction sites. This Study modeled the combined effects of soil, Surcharge loads and Hydrostatic pressure on the structural behaviours of cantilever retaining wall under varying geometric conditions. The limit state requirements for overturning, sliding and bearing pressure were studied under different geometric properties. The use of computer programming (Java) was employed for quick analyses of the conditions. This research therefore minimized the stress associated with the iterative process of design and analyses of these structures. The deductions gave range of satisfactory dimensions with respect to the height of the wall for the preliminary dimensioning state of design. This study also answered the remained unanswered question of the effects of an increasing load being supported by retaining wall. The results revealed that Cantilever retaining

wall will perform satisfactorily based on the factors of safety of 5.1 and 0.2 as against sliding and overturning respectively if soil is ignored in front of the wall with following values of Base width: For

wall supporting full submerged soil, the Base width, )005.025.1( qB ; wall supporting submerge

soil up to 0.6 of its Height, Base width, )00805.0881.0( qB and for wall with submerge soil up to

0.2 of wall height, Base width, )0091.07093.0( B . Results also showed that safety factors against

sliding and overturning increase at a decreasing rate with constant decrease in water level. This gives an indication that water level greatly affects the stability of the retaining wall, that is, the higher the water level the greater the sliding and overturning effects. Results also revealed that sliding safety factor increases constantly with Base width while factor of safety against overturning increases at an increasing rate. This also shows the severity of sliding as against overturning. Both safety factors also increase at a decreasing rate with Wall height giving an indication that the stability of cantilever retaining wall increases with its Height under the same load. For an increasing surcharge values, sliding safety factor decreases constantly while overturning decreases at a decreasing rate. This also explains why overturning is less critical as compared to sliding effect. Keywords: Retaining Wall, Hydrostatic Force, Stability, Loadings, Sliding, Overturning INTRODUCTION Retaining walls are permanent or temporary structures used to provide lateral support to the soil, liquid and other materials. These structures are used to retain earth fill or any other materials, which would not be able to stand vertically unsupported so that the ground surface at different elevations are maintained on either side of the retaining walls (Raju, 1990). Dismuke and Cornfield (1991) also described Retaining Walls as engineering structures constructed to resist lateral forces imposed by soil movement and water pressure; they are used as protection against the erosive forces of water and as a method of slope stabilization along highways, railroads and construction sites. Retaining walls are useful within the built up environment especially at bridge site,

riverbank areas and even within the house in a sloppy terrain (Oyenuga, 2001). If unrestrained, a soil embankment will relapse to its angle of repose. Some soil, such as clays have cohesion that enables vertical and near- vertical faces to remain partially intact, but even these may slump under the softening influence of groundwater. Retaining walls must adequately support its backfill without detrimental lateral movement and the surface of the backfill must not settle unduly. If water is trapped behind the retaining structure, this may also reduce the adhesion and the bearing resistance. They are often designed with great heights and length to retain the movement of the soil and the rocks in ways that are both attractive and economical. The stability of these retaining structures is vital to reduce structural failures, earthquake losses and

LAUTECH JOURNAL OF ENGINEERING AND TECHNOLOGY 7(2) 2013: 77 - 86

Adedokun, S. I. and Oluremi, J. R. /LAUTECH Journal of Engineering And Technology 7(2) 2013: 77 - 86

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post-earthquake emergency response (Green and Cameron, 2004) As a result of the dynamic nature of developments in engineering design and product development, different types of retaining walls have evolved in quick succession. Cantilever retaining walls constructed of reinforced of Portland cement concrete was the predominant type of rigid retaining walls used from about the 1920s to the 1970s. Due to superior economics in the use of material and support backfill up to 7.5m high it largely displaced the traditional gravity wall constructed of stone or unreinforced cement concrete, which may prove to be uneconomical for height above 3m (Oyenuga, 2005). According to Oyenuga (2005) and Morgenstern and Sangrey (1982), Retaining walls are broadly classified into major types as Gravity, Cantilever and Revetment walls. Delattre (2001) gave the general overview various methods used in analyzing retaining walls used over the centuries from predecessors of Coulomb to Boussinesq and the limitation of a method led to the development of another which was a continuation of work done in (Delattre,1999). The safety factor against overturning must be greater or equal to 1.5 if the soil in front of the wall is ignored and greater or equal to 2.0 if the soil is allowed in front of the wall (Alam, 1992) and Ranjan and Rao (2007). Mosley et al (1999) said that critical conditions for stability are when a maximum horizontal force acts with a minimum vertical load and when the Overturning moment is greater than Resisting moment. To guard against a stability failure, it is usual to apply conservative factors of safety to the force and loads with a value of لاf =1.6 or higher. Ranjan and Rao (2007) also made the following recommendations that Base width, B to be 0.4H to 0.7H, Projection of toe from

the base of stem to be 0.2B to 0.4B and Unit weight of granular soils may range from 16.5 to 17kN/m2 and 17 to 19kN/m2 for cohesive soils. The main objective of this study is to investigate the combined effects of soil, surcharge loads and water on the structural behaviors of cantilever retaining wall under varying geometric properties by proportioning the dimensions of the wall to allow for iterative design process to study the effect of the variations on the stability against forward sliding, overturning and bearing capacity failure. METHODOLOGY The major method employed in this research is numerical method and a computer program(Java) was developed to ease the analysis of cantilever retaining wall under varying application of loads based on the model advanced for the purpose. The project is also comparative in nature with the comparison of the changes in two or three parameters on the structural properties of the cantilever retaining walls. The types of loads allowed by the program to act on the structure (retaining walls) are hydrostatic pressure, backfill soil pressure and the self weight of the retaining walls (wall and footing). The backfill soil pressure is the pressure exerted on the structure by the retained soil which was calculated internally by the program as a function of structure lateral displacement. Self weight of the abutment was also calculated internally by the program. A structure model shown in figure 1 was used to develop a program for the calculation of the overturning moment and sliding forces on the wall under varying application of loads and geometric dimensions. The procedures followed are explained below under stability and bearing pressure analyses:

Figure 1: A Model of Cantilever Retaining Wall

q

H

WTL

B

e c d

SU

RC

HA

RG

E

DR

Y S

OIL

SU

BM

ER

GE

SO

IL

W2

W6 W5

W4 W3

W1

aH

bH Hk

Pressure

WA

TE

R


79

Stability analysis The steps used are as follows: i. The height of the retaining wall was taken to be H=3m, 5m, 7m and 9m and Width of the footing

( B ) was taken to be in the range of 5.0 to 4.1 of

wall height, Wall thickness, c = x

B where x is a

dividing factor taken as 6 in the analysis, toe width

as d =y

B , y was taken to be 3 as suggested by

Raju (1990) and width of heel, d was also used as e

=z

B , where z is also a dividing factor to allow for

varying values of e and z was used as 2 (in this study) to make heel to be half of the entire Base

width. A value of angle of internal friction ( ) was

also taken to be 30º as stated by Smith and Smith (1990) as the average value for the soil and all these are inputted into the computer program.

ii. Coefficient of active pressure, aK was determined from the equation 1:

)1(

)1(

Sin

SinKa

------------- 1

It was assumed that the effect of passive earth pressure is zero because the wall is not retaining soil in front of the stem (at toe side). iii. Lateral/horizontal earth pressure induced on the wall by the backfill soil (Pa), hydrostatic load

(Pw) and surcharge load (Ps) were calculated from equations 2 below:

Submerge Unit Weight, ' = sat 81.9 , where

)( satsat G is the saturated unit weight of the soil

aken to be 320 mkN as practical value for most

soils.

)'( baHKP aa ,

bHPw 81.9 and

qKP as ,

where a and b are multiplying factors of the wall height which demarcate the submerge portion from

the dry portion. )(G is the unit weight of the dry

soil taken to be 318 mkN for well-drained soil, q

is the surcharge load.

The Surcharge values of 30,20,10,0 and

240 mkN (Fethi, 2000) and Dicleli (2001) were

used as design practical values for uniform loads (roadway, building and stock goods) or dynamic load (traffic) and based on minimum design surcharge of

210 mkN recommended by code of practice.

After this, total horizontal force/load )( kH was

determined from the express

bHPHPKabHKbaHH wsaak 5.0)'(5.0 2222

----------------- 3

(If the wall supports the surcharge load together with the backfill soil), otherwise the surcharge effect

becomes zero and for this condition, horizontal force reduces to

bHPKabHKbaHH waak 5.0)'(5.0 2222 ------------ 4

iv. Calculation of vertical loads The vertical loads acting on the wall are loads from

surcharge ( 4W ), backfill soil ( 3W ), self weight of

the stem ( 1W ), submerge soil ( 5W ), water ( 6W ),

and self weight of the footing ( 2W ). These loads are calculated from the expression:

mcHcW )(1

BcW m2

aeHW 3

eqW 4

')(5 cbHeW

)(6 cbHeW

Where )( mm G is unit weight of concrete which was taken to be 324 mkN

Total vertical load, 654321 WWWWWWVk --------- 5 v. Checking for sliding The structure will only be stable against sliding when the frictional resisting force is greater than sliding force. These forces were calculated from:

Frictional resisting force kVF ----------- 6

Where is the coefficient of friction and its value

was taken to be 5.0 in the program. Safety factor against sliding,

ks

HFF --------------------------- 7

vi Checking for overturning effect For the wall to resist the overturning moment that may be developed at the toe, overturning moment must be less than resisting moment, that is

Resisting moment )(R ≥ Overturning moment

)( oM

226

1232236

1 5.05.0)'( HbPHPKabHKbaHM wsaao

--------- 8

)5.0)((5.0)5.0( 654321 cdeWWWWBWdcWR …………... 9

The safety factor against overturning, o

oM

RF

Bearing Pressure Analysis

---------- 2


80

The bearing pressures underneath retaining walls were assessed on the basis of serviceability limit state when determining the size of the base that is required. The analysis was based on foundations subjected to vertical load and horizontal (vertical load applied eccentrically) loads, coupled with an

overturning moment. By considering a unit length of the cantilever wall, the resultant moment about the centroidal axis of the base was calculated as:

Moment about base centre-line M

)5.05.0)(()5.05.0(5.05.0)'( 6543122

6123223

61 eBWWWWdcBWHbPHPKabHKbaHM wsaa

-------- 10 The maximum bearing pressure was calculated from the program by the expression:

21

6

B

M

B

VP

k ---------------- 11

22

6

B

M

B

VP

k ------------ 12

RESULTS AND DISCUSSION Program Structure import javax.swing.*; public class stability {public static void main (String args []) { String hi,Bi,ai,bi,µi,fi,Gi,Gisat,Gim,xi,yi,zi,qi; float H,B,a,b,µ,f,G,Gsat,Gm,x,y,z,q; double c,d,e,Gp,Pa,Ka,Ps,Pw,m,n,r,l,Hk,W1,W2,W3,W4,W5,W6,Vk,F,Fs,Mo,R,Fo,M,P1,P2; hi=JOptionPane.showInputDialog ("Enter the value of H="); Bi=JOptionPane.showInputDialog ("Enter the value of B="); ai=JOptionPane.showInputDialog ("Enter the value of a="); bi=JOptionPane.showInputDialog ("Enter the value of b="); fi=JOptionPane.showInputDialog ("Enter the value of ø= "); µi=JOptionPane.showInputDialog ("Enter the value of µ="); Gi=JOptionPane.showInputDialog ("Enter the value of G="); Gisat=JOptionPane.showInputDialog ("Enter the value of Gsat="); Gim =JOptionPane.showInputDialog ("Enter the value of Gm="); xi=JOptionPane.showInputDialog ("Enter the value of x="); yi =JOptionPane.showInputDialog ("Enter the value of y="); zi=JOptionPane.showInputDialog ("Enter the value of z="); H=Float.parseFloat (hi); B=Float.parseFloat (Bi); a=Float.parseFloat (ai); b=Float.parseFloat (bi); f=Float.parseFloat (fi); µ=Float.parseFloat (µi); G=Float.parseFloat (Gi); Gsat=Float.parseFloat (Gisat); Gm=Float.parseFloat (Gim); x=Float.parseFloat (xi); y=Float.parseFloat (yi);

z=Float.parseFloat (zi); // Processing c=B/x; d=B/y; e=B/z; // submerge Unit weight, G // Gp=Gamma prime, Gsat=Gamma Sat, Gm=Gamma m Gp=Gsat-9.81; Ka= (1 - Math.sin (3.142*f /180)) / (1 +Math.sin (3.142*f /180)); // Testing for Surcharge, q qi =JOptionPane.showInputDialog ("if the soil contains Surcharge, enter value for q=? else enter 0 (if not). Enter the value of q= "); q=Float.parseFloat (qi); n=Math.pow (H, 2); m=n*H; l=Math.pow (a, 2); r=Math.pow (b, 2); If (q!=0) { Pa=Ka*H*(a*G+b*Gp); Ps= Ka*q; Pw=9.81*b*H; // Therefore Hk=0.5*Ka*n*(l*G+r*Gp) +a*b*n*G*Ka+Ps*H+0.5*Pw*b*H; W1=c*(H-c)*Gm; W2= Gm*B*c; W3=a*e*H*G; W4=e*q; W5=e*(b*H-c)*Gp; W6=9.81*e*(b*H-c); Vk=W1+W2+W3+W4+W5+W6; F=µ*Vk; Fs=F/Hk; Mo=m*Ka*(l*G+r*Gp)/6+0.5*a*b*m*G*Ka+0.5*Ps*n+Pw*r*n/6; R=W1*(0.5*c+d) +0.5*W2*B+ (W3+W4+W5+W6)*(0.5*e+c+d); Fo=R/Mo; M=m*Ka*(l*G+r*Gp)/6+0.5*a*b*m*G*Ka+0.5*Ps*n+Pw*r*n/6+W1* (0.5*B-0.5*c-d)-(W3+W4+W5+W6)*(0.5*B-0.5*e); }//End of if when there is surcharge else { Pa=Ka*H*(a*G+b*Gp); Pw=9.81*b*H;


81

Hk=0.5*n*Ka*(l*G+r*Gp) +a*b*n*G*Ka+0.5*Pw*b*H; W1=c*(H-c)*Gm; W2= Gm*B*c; W3=a*e*H*G; W5=e*(b*H-c)*Gp; W6=9.81*e*(b*H-c); Vk= W1+W2+W3+W5+W6; F=µ*Vk; Fs=F/Hk; Mo=m*Ka*(l*G+r*Gp)/6+0.5*a*b*m*G*Ka+Pw*r*n/6;

R= W1*(0.5*c+d) +0.5*W2*B+ (W3+W5+W6)*(0.5*e+c+d); Fo=R/Mo; M=m*Ka*(l*G+r*Gp)/6+0.5*a*b*m*G*Ka+Pw*r*n/6+W1* (0.5*B-0.5*c-d) - (W3+W5+W6)*(0.5*B-0.5*e); }//end of else P1=Vk/B+ (6*M)/ (Math.pow (B, 2)); P2=Vk/B-(6*M)/(Math.pow(B, 2));

//Displaying Result System.out.println ("Output Results"); System.out.println (" Ka = " +Ka); System.out.println (" Hk = " +Hk); System.out.println (" Vk = " +Vk); System.out.println (" F = " +F); System.out.println (" R = " +R); System.out.println (" Mo = " +Mo);

System.out.println (" M = " +M); System.out.println (" Fs = " +Fs); System.out.println (" Fo = " +Fo); System.out.println (" P1 = " +P1); System.out.println (" P2 = " +P2); System.exit (0); } }

Samples of the Output for the Combined Effects of Soil, Surcharge and Water Microsoft Windows [Version 6.0.6001] Copyright (c) 2006 Microsoft Corporation. All rights reserved. C:\Users\SOLOMON COMPUTERS>cd.. C:\Users>cd.. C:\>cd j2* C:\j2sdk1.4.1_01>cd bin C:\j2sdk1.4.1_01\bin>java stability ========Input Values======= H= 3.0 B= 1.5 a= 0.0 b= 1.0 x= 6.0 y= 3.0 z= 2.0 ° = 30.0 Á = 0.5 G = 18.0 Gm = 24.0 Gsat = 20.0 q = 10.0 ========Output Results======= Ka = 0.3332810738372141 Hk = 69.42603585592187 Vk = 74.25 F = 37.125 R = 71.90625 Mo = 74.4252519634801 M = 58.20650196348009 Fs = 0.5347417513084658 Fo = 0.9661539343566328 P1 = 204.71733856928026 P2 = -105.71733856928026

C:\j2sdk1.4.1_01\bin>java stability ========Input Values======= H= 3.0 B= 1.8 a= 0.0 b= 1.0 x= 6.0 y= 3.0 z= 2.0 ° = 30.0 Á = 0.5 G = 18.0 Gm = 24.0 Gsat = 20.0 q = 10.0 ========Output Results======= Ka = 0.3332810738372141 Hk = 69.42603585592187 Vk = 89.99999607801442 F = 44.99999803900721 R = 104.00399112832565 Mo = 74.4252519634801 M = 51.421253442986554 Fs = 0.6481717915220536 Fo = 1.397428807891166 P1 = 145.2245476037829 P2 = -45.22454931244937


82

C:\j2sdk1.4.1_01\bin>java stability ========Input Values======= H= 3.0 B= 2.1 a= 0.0 b= 1.0 x= 6.0 y= 3.0 z= 2.0 ° = 30.0 Á = 0.5 G = 18.0 Gm = 24.0 Gsat = 20.0 q = 10.0 ========Output Results======= Ka = 0.3332810738372141 Hk = 69.42603585592187 Vk = 106.0499956905842 F = 53.0249978452921 R = 142.1857400884332 Mo = 74.4252519634801 M = 43.592004264725965 Fs = 0.7637624299237474 Fo = 1.9104502347966879 P1 = 109.80885496781349 P2 = -8.808854485299655 C:\j2sdk1.4.1_01\bin>java stability ========Input Values======= H= 3.0 B= 2.4 a= 0.0 b= 1.0 x= 6.0 y= 3.0 z= 2.0 ° = 30.0 Á = 0.5 G = 18.0 Gm = 24.0 Gsat = 20.0 q = 10.0 ========Output Results======= Ka = 0.3332810738372141 Hk = 69.42603585592187 Vk = 122.40000438690187 F = 61.200002193450935 R = 186.52801146411912 Mo = 74.4252519634801 M = 34.77724938283734 Fs = 0.8815137064783273 Fo = 2.506246287962142 P1 = 87.22629836276582 P2 = 14.7737012398699

C:\j2sdk1.4.1_01\bin>java stability ========Input Values======= H= 3.0 B= 2.7 a= 0.0 b= 1.0 x= 6.0 y= 3.0 z= 2.0 ° = 30.0 Á = 0.5 G = 18.0 Gm = 24.0 Gsat = 20.0 q = 10.0 ========Output Results======= Ka = 0.3332810738372141 Hk = 69.42603585592187 Vk = 139.05000440478327 F = 69.52500220239163 R = 237.10726372513193 Mo = 74.4252519634801 M = 25.035499954237302 Fs = 1.0014254932641573 Fo = 3.1858442863113003 P1 = 72.10534975064526 P2 = 30.894651693111687 C:\j2sdk1.4.1_01\bin>java stability ========Input Values======= H= 3.0 B= 3.0 a= 0.0 b= 1.0 x= 6.0 y= 3.0 z= 2.0 ° = 30.0 Á = 0.5 G = 18.0 Gm = 24.0 Gsat = 20.0 q = 10.0 ========Output Results======= Ka = 0.3332810738372141 Hk = 69.42603585592187 Vk = 156.0 F = 78.0 R = 294.0 Mo = 74.4252519634801 M = 14.425251963480093 Fs = 1.123497820930918 Fo = 3.9502721488166888 P1 = 61.616834642320065 P2 = 42.383165357679935


83

0100200300400500600700

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Fri

cti

on

al

resis

tin

g

forc

e,F

(kN

/m)

Coefficient,k …

F(H=3m)F(H=5m)F(H=7m)F(H=9m)

C:\j2sdk1.4.1_01\bin>java stability ========Input Values======= H= 5.0 B= 2.5 a= 0.0 b= 1.0 x= 6.0 y= 3.0 z= 2.0 ° = 30.0 Á = 0.5 G = 18.0 Gm = 24.0 Gsat = 20.0 q = 10.0 ========Output Results======= Ka = 0.3332810738372141 Hk = 181.74073047187585 Vk = 197.91666532556212 F = 98.95833266278106 R = 317.2742993156943 Mo = 316.78792886301034 M = 246.90945741689023 Fs = 0.5445027782481304 Fo = 1.001535318768078 P1 = 316.1997452504395

P2 = -157.8664129899897

Behaviour of Frictional Resisting Force with Base

Width and Wall Height

The behaviour of Frictional resisting force with both Base width and Wall height is expressed graphically of Figures 2 to 4, which shows a linear relationship with Base width and non-linear relationship with Height of the retaining wall. This revealed that Frictional resisting force increases constantly with Base width but increases at an increasing rate with Wall height. For a particular wall height, Frictional resisting force increases constantly while Horizontal thrust remains unchanged but increases at an increasing rate with constant increase in Wall height. Figure 5 shows the behaviour of the Frictional resisting force both increase in surcharge values and water table levels; it is clearly shown that Resisting force decreases constantly with a constant decrease in water level but increases constantly with an increasing surcharge loads. This figure also revealed that the higher the load being supported by the retaining wall, the higher the value of the resisting force but the greater the horizontal thrust on the wall and thereby leads to greater tendencies of failure of the retaining wall.

Figure 2: Frictional resisting force against Base width (for a= 0.0 and q=10kN/m2)




84

Figure 5: Behaviour of Resisting force against Base width (H=3m) Figures 6 to 7 showed that resisting moment behaves non-linearly with both Base width and Wall height, giving a positive curvature. Results showed that Resisting moment increases at an increasing rate with both Base width and Wall height. Overturning moment remains unchanged for a particular wall height despite an increasing value of Base width but increases an increasing rate with constant increase in Wall height. Figure 3.8 showed that resisting moment

decreases constantly with constant increase in water table level but increases constantly with constant increase in surcharge loads. Result also revealed that the Overturning moment reduces at a greater decreasing rate with a constant decrease in water level and this shows that the higher the water table level the greater will the effect of Overturning on the retaining wall.

Figure 5: Behaviour of Resisting force against Base width (H=3m)

Figure 6: Resisting Moment versus Base width (for a=0.0 and q= 10kN/m2)



0

500

1000

0.7 0.9 1.1 1.3 1.5

Res

isti

ng

m

om

en

t,R

(kN

m/m

)

Coefficient,k …

R(a=0.0,q=10)R(a=0.4,q=10)R(a=0.8,q=10)R(a=0.0,q=20)R(a=0.4,q=20)

Figure 9: Behaviour of Resisting Moment against Base width (H=3m)


85

Figures 8 and 9 showed the behaviour of the Safety factors against Overturning and Sliding with Base width, it is revealed that the two Safety factors increases at a decreasing rate with constant decrease in water level. This gives an indication that water level greatly affects the stability of the retaining wall, that is, the higher the water level the greater the sliding and overturning effects. Results also revealed that sliding safety factor increases constantly with Base width while Factor of safety against overturning increases at an increasing rate. This also shows the severity of Sliding as against Overturning. Both safety factors also increase at a decreasing rate with Wall height giving an indication that the stability of cantilever retaining wall increases with its Height

under the same load. For an increasing Surcharge values, Sliding safety factor decreases constantly while overturning decreases at a decreasing rate. This also explains why Overturning is less critical as compared to Sliding effect. The satisfactory values of these factors (the value of Base width at the safety factors of 1.5 and 2.0 for Sliding and Overturning respectively) are given below in figures 10 to 12: For wall supporting full submerged soil, the Base width, B= (1.25+0.005q) H; wall supporting submerge soil up to 0.6 of its Height, Base width, B= (0.881+0.00805q) and for wall with submerge soil up to 0.2 of wall height, Base width, B= (0.7093+0.0091q).

CONCLUSION AND RECOMMENDATION Results revealed that the higher the load being supported by retaining wall the lower the resistance offered against sliding and overturning. It also showed clearly that Frictional resisting force increases constantly with Base width but increases at an increasing rate with Wall height. This study also revealed that Resisting moment increases at an increasing rate with both Base width and Wall

height. Overturning moment remains unchanged for a particular wall height despite an increasing value of Base width but increases at an increasing rate with constant increase in Wall height. Results also showed that Safety factors against sliding and overturning increase at a decreasing rate with constant decrease in water level. This gives an indication that water level greatly affects the stability of the retaining wall, that is, the higher the water level the greater the

Figure 11: Factor of Safety against Sliding versus Base width (for H=3m)

Figure 10: Factor of Safety against Sliding versus Base width (for q= 10kN/m2)

Figure 12: Factor of Safety against Overturning versus Base width ( for q= 10kN/m2)

Figure 3.12: Factor of Safety against Overturning versus Base width (for H=3m)


86

sliding and overturning effects. Results further revealed that sliding safety factor increases constantly with Base width while Factor of safety against overturning increases at an increasing rate. This also shows the severity of Sliding as against Overturning. Both safety factors also increase at a decreasing rate with Wall height giving an indication that the stability of cantilever retaining wall increases with its Height under the same load. For an increasing Surcharge values, Sliding safety factor decreases constantly while overturning decreases at a decreasing rate. This also explains why Overturning is less critical as compared to Sliding effect. REFERENCES Adedokun, S.I. (2009) “Modeling of the Structural

Stability of Cantilever retaining walls under varying applied loading conditions”, An Unpublished M.Sc Dissertation, Civil Engineering Dept., University of Ibadan, Nigeria.

Alam, S. (1992) Modern Geotechnical Engineering, 3rd Edition, Jourpur, CBS Publishers & Distributors Pvt. Ltd

Delatre, L. (2001) “Century of design methods for retaining walls”, Laboratore central des ponts et chausses, BLPC, 234 Pages.

Dicleli, M. (2001) “Computer-aided limit states analysis of bridge abutments” Dept. of Civil Eng. and Construction, Bradley University, Peoria, Illinois 61625, USA. Retrieved November 6, 2008 from: www.civag.unimelb.edu.au/ejse/Archives/Fultext/200106.pdf

Dismuke, T.D. and Cornfield, G.M. (1991) “Retaining structures and excavations in famg” Foundation Engineering Handbook, 2nd edition, Van Nostrand Reinhold, new York, pp 447-510

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the combined effects of soil, water and surcharge … · 2019. 10. 27. · jekayinfa, s.o. and...

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